# Computing the Lines Piercing Four Lines

### http://www2.eecs.berkeley.edu/Pubs/TechRpts/1992/CSD-92-665.pdf

Given four distinct lines in R^3 there exist zero, one, two, or various infinities of lines incident on the given lines. We wish to characterize and compute the set of incident lines in a numerically stable way. We use the Plucker coordinatization of lines to cast this problem as a null-space computation in R^5, and show how the singular value decomposition (SVD) yields a simple, stable characterization of the incident lines. Finally, we enumerate the types of input degeneracies that may arise, and describe the solution set of lines in each case.

BibTeX citation:

```@techreport{Teller:CSD-92-665,
Author = {Teller, Seth J. and Hohmeyer, Michael E.},
Title = {Computing the Lines Piercing Four Lines},
Institution = {EECS Department, University of California, Berkeley},
Year = {1991},
Month = {Jan},
URL = {http://www2.eecs.berkeley.edu/Pubs/TechRpts/1991/6126.html},
Number = {UCB/CSD-92-665},
Abstract = {Given four distinct lines in R^3 there exist zero, one, two, or various infinities of lines incident on the given lines. We wish to characterize and compute the set of incident lines in a numerically stable way. We use the Plucker coordinatization of lines to cast this problem as a null-space computation in R^5, and show how the singular value decomposition (SVD) yields a simple, stable characterization of the incident lines. Finally, we enumerate the types of input degeneracies that may arise, and describe the solution set of lines in each case.}
}
```

EndNote citation:

```%0 Report
%A Teller, Seth J.
%A Hohmeyer, Michael E.
%T Computing the Lines Piercing Four Lines
%I EECS Department, University of California, Berkeley
%D 1991
%@ UCB/CSD-92-665
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/1991/6126.html
%F Teller:CSD-92-665
```